# Deep Implicit Surface Point Prediction Networks

arXiv: https://arxiv.org/abs/2106.05779 · HTML: https://mlsanity.com/paper/2106.05779/

## Key facts

- Cited by 40 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 47 references that are in the map.
- First posted on arXiv 10 Jun 2021.

## Builds on (most cited first, 24 of 24)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Billion-scale similarity search with GPUs](https://mlsanity.com/paper/1702.08734/) (2017)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [Pixel2Mesh: Generating 3D Mesh Models from Single RGB Images](https://mlsanity.com/paper/1804.01654/) (2018)
- [3D-R2N2: A Unified Approach for Single and Multi-view 3D Object Reconstruction](https://mlsanity.com/paper/1604.00449/) (2016)
- [AtlasNet: A Papier-Mach'e Approach to Learning 3D Surface Generation](https://mlsanity.com/paper/1802.05384/) (2018)
- [SAL: Sign Agnostic Learning of Shapes from Raw Data](https://mlsanity.com/paper/1911.10414/) (2019)
- [Implicit Functions in Feature Space for 3D Shape Reconstruction and Completion](https://mlsanity.com/paper/2003.01456/) (2020)
- [Neural Unsigned Distance Fields for Implicit Function Learning](https://mlsanity.com/paper/2010.13938/) (2020)
- [Pix3D: Dataset and Methods for Single-Image 3D Shape Modeling](https://mlsanity.com/paper/1804.04610/) (2018)
- [BSP-Net: Generating Compact Meshes via Binary Space Partitioning](https://mlsanity.com/paper/1911.06971/) (2019)
- [CvxNet: Learnable Convex Decomposition](https://mlsanity.com/paper/1909.05736/) (2019)
- [SALD: Sign Agnostic Learning with Derivatives](https://mlsanity.com/paper/2006.05400/) (2020)
- [Deep Mesh Reconstruction from Single RGB Images via Topology Modification Networks](https://mlsanity.com/paper/1909.00321/) (2019)
- [Image-based 3D Object Reconstruction: State-of-the-Art and Trends in the Deep Learning Era](https://mlsanity.com/paper/1906.06543/) (2019)
- [Robust Watertight Manifold Surface Generation Method for ShapeNet Models](https://mlsanity.com/paper/1802.01698/) (2018)
- [Style-based Point Generator with Adversarial Rendering for Point Cloud Completion](https://mlsanity.com/paper/2103.02535/) (2021)
- [Intrinsic3D: High-Quality 3D Reconstruction by Joint Appearance and Geometry Optimization with Spatially-Varying Lighting](https://mlsanity.com/paper/1708.01670/) (2017)
- [Appearance Consensus Driven Self-Supervised Human Mesh Recovery](https://mlsanity.com/paper/2008.01341/) (2020)

## Built on by (most cited first, 30 of 40)

- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [AutoSDF: Shape Priors for 3D Completion, Reconstruction and Generation](https://mlsanity.com/paper/2203.09516/) (2022)
- [MeshUDF: Fast and Differentiable Meshing of Unsigned Distance Field Networks](https://mlsanity.com/paper/2111.14549/) (2021)
- [CAP-UDF: Learning Unsigned Distance Functions Progressively from Raw Point Clouds with Consistency-Aware Field Optimization](https://mlsanity.com/paper/2210.02757/) (2022)
- [GIFS: Neural Implicit Function for General Shape Representation](https://mlsanity.com/paper/2204.07126/) (2022)
- [DrapeNet: Garment Generation and Self-Supervised Draping](https://mlsanity.com/paper/2211.11277/) (2022)
- [NeUDF: Leaning Neural Unsigned Distance Fields with Volume Rendering](https://mlsanity.com/paper/2304.10080/) (2023)
- [Learning a More Continuous Zero Level Set in Unsigned Distance Fields through Level Set Projection](https://mlsanity.com/paper/2308.11441/) (2023)
- [NeAT: Learning Neural Implicit Surfaces with Arbitrary Topologies from Multi-view Images](https://mlsanity.com/paper/2303.12012/) (2023)
- [ISP: Multi-Layered Garment Draping with Implicit Sewing Patterns](https://mlsanity.com/paper/2305.14100/) (2023)
- [3PSDF: Three-Pole Signed Distance Function for Learning Surfaces with Arbitrary Topologies](https://mlsanity.com/paper/2205.15572/) (2022)
- [Few 'Zero Level Set'-Shot Learning of Shape Signed Distance Functions in Feature Space](https://mlsanity.com/paper/2207.04161/) (2022)
- [Robust Zero Level-Set Extraction from Unsigned Distance Fields Based on Double Covering](https://mlsanity.com/paper/2310.03431/) (2023)
- [Representing 3D Shapes with Probabilistic Directed Distance Fields](https://mlsanity.com/paper/2112.05300/) (2021)
- [Neural Vector Fields: Implicit Representation by Explicit Learning](https://mlsanity.com/paper/2303.04341/) (2023)
- [DeepMesh: Differentiable Iso-Surface Extraction](https://mlsanity.com/paper/2106.11795/) (2021)
- [DeepCurrents: Learning Implicit Representations of Shapes with Boundaries](https://mlsanity.com/paper/2111.09383/) (2021)
- [Mixing-Denoising Generalizable Occupancy Networks](https://mlsanity.com/paper/2311.12125/) (2023)
- [What's the Situation with Intelligent Mesh Generation: A Survey and Perspectives](https://mlsanity.com/paper/2211.06009/) (2022)
- [DUDF: Differentiable Unsigned Distance Fields with Hyperbolic Scaling](https://mlsanity.com/paper/2402.08876/) (2024)
- [SuperUDF: Self-supervised UDF Estimation for Surface Reconstruction](https://mlsanity.com/paper/2308.14371/) (2023)
- [Unsigned Orthogonal Distance Fields: An Accurate Neural Implicit Representation for Diverse 3D Shapes](https://mlsanity.com/paper/2403.01414/) (2024)
- [Neural Volumetric Mesh Generator](https://mlsanity.com/paper/2210.03158/) (2022)
- [MARF: The Medial Atom Ray Field Object Representation](https://mlsanity.com/paper/2307.00037/) (2023)
- [Neural Vector Fields: Generalizing Distance Vector Fields by Codebooks and Zero-Curl Regularization](https://mlsanity.com/paper/2309.01512/) (2023)
- [A Latent Implicit 3D Shape Model for Multiple Levels of Detail](https://mlsanity.com/paper/2409.06231/) (2024)
- [Automated Reconstruction of 3D Open Surfaces from Sparse Point Clouds](https://mlsanity.com/paper/2210.15059/) (2022)
- [PU-Ray: Domain-Independent Point Cloud Upsampling via Ray Marching on Neural Implicit Surface](https://mlsanity.com/paper/2310.08755/) (2023)
- [DITTO: Dual and Integrated Latent Topologies for Implicit 3D Reconstruction](https://mlsanity.com/paper/2403.05005/) (2024)
- [Surface Reconstruction from Point Clouds via Grid-based Intersection Prediction](https://mlsanity.com/paper/2403.14085/) (2024)

## Abstract (arXiv)

Deep neural representations of 3D shapes as implicit functions have been shown to produce high fidelity models surpassing the resolution-memory trade-off faced by the explicit representations using meshes and point clouds. However, most such approaches focus on representing closed shapes. Unsigned distance function (UDF) based approaches have been proposed recently as a promising alternative to represent both open and closed shapes. However, since the gradients of UDFs vanish on the surface, it is challenging to estimate local (differential) geometric properties like the normals and tangent planes which are needed for many downstream applications in vision and graphics. There are additional challenges in computing these properties efficiently with a low-memory footprint. This paper presents a novel approach that models such surfaces using a new class of implicit representations called the closest surface-point (CSP) representation. We show that CSP allows us to represent complex surfaces of any topology (open or closed) with high fidelity. It also allows for accurate and efficient computation of local geometric properties. We further demonstrate that it leads to efficient implementation of downstream algorithms like sphere-tracing for rendering the 3D surface as well as to create explicit mesh-based representations. Extensive experimental evaluation on the ShapeNet dataset validate the above contributions with results surpassing the state-of-the-art.